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The parametric equations for a line L1 are as follows: x =2+6t y =-3 6t 2 =4+6tLet Lz be the line parallel to L1 and passing through the point (3,~5, ~2) . Find the...

Question

The parametric equations for a line L1 are as follows: x =2+6t y =-3 6t 2 =4+6tLet Lz be the line parallel to L1 and passing through the point (3,~5, ~2) . Find the point P on Lz whose x-coordinate is 12. P = (12, 0 . 0 )

The parametric equations for a line L1 are as follows: x =2+6t y =-3 6t 2 =4+6t Let Lz be the line parallel to L1 and passing through the point (3,~5, ~2) . Find the point P on Lz whose x-coordinate is 12. P = (12, 0 . 0 )



Answers

Find parametric equations for the line that passes through the point $P$ and is parallel to the vector $\mathbf{v} .$ $$ P(1,0,-2), \quad \mathbf{v}=\langle 3,2,-3\rangle $$

For this exercise. We want to find the line that is passing through the points to 12 and two We wish is equal to 01 negative three. So, sense it passes through these points. It is parallel to the vector P two, which is equal to zero minus two more, one minus minus bone. Negative. Three minus Get up to which is an equal to two. Uh, excuse me. This becomes a plus. So this is to and this becomes negative. Three plus two is negative one. So now we have a point. Let's choose P of the land passes through. And a factor too, Which is It is parallel. So now we can find the Parametric equations very easily. X is equal to two minus two t because we're looking the first coordinated. The first component here Why is equal to negative one plus two. T and Z is equal to negative two minus one team or no tu minus T. And these are the parametric equations off the line that we were looking for

No I got a problem for again. The problem for is the same thing. It passes to the going to Judo 14 and -10. And again it's parlor too. X equals 2 -1 plus two. T Why equal to 6- Treaty? And G equals 23 plus 90. Right now again with the same thing for the parameter equation. What we do can you do the same thing? This is my remember and this the vicar be here is two -3 and nine so He can parliamentary question. It just takes -0/2. The same as Y -14/-3. The same as G plus 10 overnight. And again to use a secret to T. So access to T. Why is -3 t plus 14 And G. is 90 -10. This is how the question looks like. And for the better equation like we said before this is a not some T. V. So this is due to wake up plus 14 Jacob Afghanistan K cap nasty times to wake up minus T. Jacob plus nine. Kick and dissect. That's the answer.

For this exercise. We want to find a line that passes through the points p 12 16 18 and cue, which is 12 noted 60 First, we confined the Nectar B Q, for which the line is parallel. So this is given by 12 months. 12 negative six months 16 zero minus 18 which finally yields zero negative. 22. They're gonna 18 and thus we have a vector to which the lines parallel on the point Who is the line passes? Which gives us the following Parametric Equations X is equal to 12 plus zero t, which is just fell. Why is equal to 16 minus 22. T and Z is equal to 18 minus 18 t. So these are the Parametric equations for this line, and this is our final answer.

This exercise for the point P 3 to 1 on the Vector V, which is equal to zero, longs for to. We want to find a line that passes through P and eyes panel TV and want to find the equations for that line. So we have, as we saw before, X is equal to 30 T or just three. Why is equal to two minus 40? There's no simplification to be done. For that Z is equal to one plus two t where t is the parameter for the equations. So these are the car metric equations that describe the line that we wanted.


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